The first non-Cartesian coordinate system students encounter in physics is the simple polar system with a radial and angular coordinate. The first denotes distance from the origin, while the second indicates the azimuthal angle from some reference direction. This system is extended into three dimensions in two different ways. The first, spherical polar coordinates, incorporates an elevation angle above the plane, which is variously referred to as the latitude or inclination. However, the two original coordinates maintain their meanings, so it is appropriate to use the same names for those directions: radial and azimuthal. One speaks of the (r, θ, ɸ) coordinates sensibly as “radius, latitude, and azimuth,” with adjective forms “radial, latitudinal, and azimuthal.” (Physicists are in the unfortunate habit of using θ for the azimuthal coordinate in elementary two-dimensional problems, then introducing ɸ for azimuth and reassigning θ to be the complement of the elevation...

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